Geodesic orbit and weakly symmetric spray manifolds

Xiyun Xu; Ming Xu

doi:10.5802/crmath.673

Article de recherche - Géométrie et Topologie

Geodesic orbit and weakly symmetric spray manifolds
[Orbite géodésique et variétés de spray faiblement symétriques]

Xiyun Xu ¹ ; Ming Xu ¹

¹ School of Mathematical Sciences, Capital Normal University, Beijing 100048, P.R. China

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 337-344.

Abstract (VO)
Résumé

In this paper, we introduce the geodesic orbit and weakly symmetric properties in homogeneous spray geometry. When a homogeneous spray manifold is endowed with a reductive decomposition, we use the spray vector field to describe these properties, and prove that a weakly symmetric spray manifold must be geodesic orbit, which generalizes its analog in homogeneous Riemannian and Finsler geometries.

Dans cet article, nous introduisons l’orbite géodésique et les propriétés faiblement symétriques dans la géométrie homogène de spray. Lorsqu’un collecteur homogène de spray est doté d’une décomposition réductrice, nous utilisons le champ de vecteurs de spray pour décrire ces propriétés, et prouvons qu’un collecteur de spray faiblement symétrique doit avoir une orbite géodésique, ce qui généralise son analogue dans les géométries homogènes de Riemann et de Finsler.

Reçu le : 2024-04-07
Révisé le : 2024-08-01
Accepté le : 2024-08-07
Publié le : 2025-05-20

DOI : 10.5802/crmath.673

Classification : 22E46, 53C30
Keywords: Homogeneous geodesic, homogeneous spray manifold, weakly symmetric space, geodesic orbit space, spray structure, spray vector field
Mots-clés : Géodésique homogène, espace de pulvérisation homogène, espace faiblement symétrique, espace d’orbite géodésique, structure de pulvérisation, champ de vecteurs de pulvérisation

Affiliations des auteurs :

Xiyun Xu ¹ ; Ming Xu ¹

¹ School of Mathematical Sciences, Capital Normal University, Beijing 100048, P.R. China

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2025__363_G4_337_0,
     author = {Xiyun Xu and Ming Xu},
     title = {Geodesic orbit and weakly symmetric spray manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {337--344},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     year = {2025},
     doi = {10.5802/crmath.673},
     language = {en},
}

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Xiyun Xu; Ming Xu. Geodesic orbit and weakly symmetric spray manifolds. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 337-344. doi : 10.5802/crmath.673. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.673/

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